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In this brief, we extend the simulation-based approximate dynamic programming (ADP) method to optimal feedback control of fed-batch reactors. We consider a free-end problem, wherein the batch time is considered in finding the optimal feeding strategy in addition to the final time productivity. In ADP, the optimal solution is parameterized in the form of profit-to-go function. The original definition of profit-to-go is modified to include the decision of batch termination. Simulations from heuristic feeding policies generate the initial profit-to-go versus state data. An artificial neural network then approximates profit-to-go as a function of process state. Iterations of the Bellman equation are used to improve the profit-to-go function approximator. The profit-to-go function approximator thus obtained, is then implemented in an online controller. This method is applied to cloned invertase expression in Saccharomyces cerevisiae in a fed-batch bioreactor.